A268813 Decimal expansion of sum(k>=0, 1/C(k)), where C(k) is a Catalan Number (A000108).

2, 8, 0, 6, 1, 3, 3, 0, 5, 0, 7, 7, 0, 7, 6, 3, 4, 8, 9, 1, 5, 2, 9, 2, 3, 6, 7, 0, 0, 6, 3, 1, 8, 0, 3, 2, 5, 4, 5, 9, 5, 8, 4, 9, 9, 9, 1, 5, 2, 3, 2, 9, 1, 4, 4, 6, 9, 7, 7, 2, 6, 6, 3, 7, 9, 5, 0, 2, 7, 6, 9, 6, 9, 3, 8, 9, 4, 9, 0, 6, 1, 4, 9, 7, 0, 7, 2, 2, 2, 1, 6, 9, 8, 3, 1, 3, 7, 8, 5, 2, 8, 2

Offset: 1

Author

Jean-François Alcover, Feb 14 2016

Keywords

• nonn
• cons

Examples

			2.80613305077076348915292367006318032545958499915232914469772663795...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000
• Eric Weisstein's MathWorld, Catalan Number.
• Wikipedia, Catalan number

Crossrefs

Cf. A000108, A121839 (which is the main entry for this constant).

Programs

Magma

SetDefaultRealField(RealField(100)); R:=RealField(); 2 + 4*Pi(R)/(9*Sqrt(3)); // G. C. Greubel, Nov 04 2018

Mathematica

RealDigits[2 + 4*Pi/(9*Sqrt[3]), 10, 102][[1]]

PARI

default(realprecision, 100); 2 + 4*Pi/(9*sqrt(3)) \\ G. C. Greubel, Nov 04 2018

Formula

Equals 2 + 4*Pi/(9*sqrt(3)) = 1 + A121839.

Also equals 2F1(1, 2; 1/2; 1/4), where 2F1 is the hypergeometric function 2F1.